The atomic force microscope (AFM) was developed in 1986 by Binnig, Quate and Gerber. The AFM utilizes a sharp probe moving over the surface of a sample under inspection, for measuring the sample's topography and dimensions of the sample. The probe is a tip on the end of a cantilever, which bends in response to a force acting between the tip and the sample.
The force experienced by the cantilever varies depends on the degree of separation between the tip and the sample. A repulsive force dominates at small interatomic distances, and it increases exponentially with decreasing separation. On the other hand, an attractive force (van der Waals force) dominates at larger separations.
The measuring modes of the AFM are roughly classified into a contact mode and a tapping mode. In the contact mode, the AFM tip makes soft physical contact with the sample. As the tip approaches the sample surface, the interatomic forces become very strongly repulsive. Since the cantilever has a low spring constant (lower than the effective spring constant holding the atoms of the sample together), the forces will cause the cantilever to bend following the surface topography of the sample. Therefore, the detection of the position of the cantilever leads to a topographic map of the sample surface.
In most the contact mode AFMs, the position of the cantilever is detected with optical techniques. A common detecting scheme is equipping an AFM with a laser beam. The laser beam is reflected onto a position-sensitive photo-detector (photodiode) by a back side of the cantilever. The AFM can generate the topographic data by operating in one of two modes: a constant-height mode or a constant-force mode. In the constant-height mode, the spatial variation of the cantilever deflection can be used directly to generate the topographic data as a scanner height is fixed during the scan.
In the constant-force mode, the deflection of the cantilever can be used as input to a feedback circuit that moves the scanner up and down in a device-defined Z-direction, responding to the topography of the sample by keeping the cantilever deflection constant. In this way, the total force applied by the cantilever onto the sample is kept constant. The constant-force mode is generally preferred for most applications.
The tapping mode is another common mode used in AFM. When operated in air or other gases, the cantilever is oscillated at its resonant frequency (often hundreds of kilohertz) and is positioned above the surface of the sample so that it only taps the surface for a very small fraction of its oscillation period. In the tapping mode, the tip still contacts the sample in the sense defined hereinabove. However, the very short time over which this contact occurs means that lateral forces are dramatically reduced as the tip scans over the surface. When imaging samples that are poorly immobilized or soft, the tapping mode may be a far better choice than the contact mode for imaging.
The AFM tip is perpendicular to the sample surface when the AFM probes the sample surface. If the sample surface is smooth, the tip-sample interatomic force is exerted to the AFM tip along the Z-direction only. Therefore, this interatomic force also bends or oscillates the cantilever along the Z-direction rather than the X- or Y-directions. Along the same Z-direction, the oscillating or bending signals of the cantilever, detected by a detector of the AFM, are actually the signals from the sample surface. Gathering and processing of the oscillating signals or bending signals by a calculator provides an accurate topographic map of the actual sample surface.
If the sample surface is not smooth but curved, the tip-sample interatomic force is exerted to the AFM tip along not only the Z-direction but also the X- or Y-directions. In this case, the tip-sample interatomic force still bends or oscillates the cantilever only along the Z-direction. As a result, the tip-sample interatomic force experienced by the cantilever is smaller than the tip-sample interatomic force experienced by the tip. However, the detector of the AFM cannot determine the difference.
The curved sample surface substantially tilts at an angle. If this angle is relatively large, the interatomic force exerted up to the AFM tip along the X- or Y-directions is also large. Such angle reduces the interatomic force along the Z-direction, and therefore decreases the accuracy of the resultant topographic map.
Thus, what is needed is an AFM which can accurately measure a curved surface topography of a sample.